Hello, Welcome to Just Answer!
What you describe is a very difficult predicament to be in- for both of you.
I can only imagine your boyfriend is trying to avoid a big blow up- knowing her history of aggression- Yikes! However, she will continue to be in his life, and as a result, your life, until he's very clear and assertive with her. She will be as involved as he allows her to be. She is likely playing on his guilt, you mentioned he felt, for "breaking her heart".
If she is truly "psychotic", more of a reason he needs to set really clear boundaries with her- or cut off the contact completely. I can understand your upset with this- probably thinking he would just tell her to go away, because the two of you are so committed to one another.
This must be really stressful for him, and you, of course. The sooner the better that he tells her clearly he's in a committed relationship, and that he does not want to risk losing you. If he consistently gives her those clear messages, even knowing she may be persistent in her attempts to stay involved with him, she will be forced to look for support elsewhere. This will not be easy for him, because of her emotional health issues. She will make it difficult for him, and he needs to be prepared for that.
It may not be "pretty" when he sets those expectations and boundaries, because she may push it, and be so persistent and demanding. He will need to stick to the clear message and not get into conversations with her. Coming up with a statement ahead of time, even writing it down, may help him be prepared.
It may help him for you to validate how difficult this must be for him. Telling him, "I know this is very difficult for you, that you feel obligated in some way to support her, but our relationship means a lot to me, and I don't want to risk jeopardizing something so important to me, to us". If he supports her emotionally he's not "available" to you or the relationship. If he feels so guilty, including that in his statement to her may allow him to put some closure on this.
If she becomes threatening, or aggressive, he will need to be clear with her that he will not tolerate that, and will call the police if it continues. She sounds like she is capable of lashing out- "arrested for beating up somebody?" Because of the risk here, it's even more important for him to be really clear and assertive. Of course it's not easy, and most of us want to avoid a conflict, avoid confrontation, but your relationship is on the line here.
By texting, talking, allowing her in his home, he is giving her the message that she decides how this is going to go- he just goes along for the ride. She preys on his passivity/ and kindness. She may use her mental and physical health as a way to manipulate him, something he will need to be prepared for. He is not responsible for her being "psychotic", none of us are that powerful to make that happen.
Something to consider, if this was reversed, and it was you in his position, how would he react? I don't think your concerns are to "control" him, you worry about your relationship.
Consider saying: "I love that you are so giving and caring. It's one of the things that attracted me to you. I trust you so much. But I'm getting concerned about your involvement with ___. I don't feel like she respects our relationship, and I need you to set stronger boundaries" It's up to him to set the boundaries and for you to be able to stay out of it.
There is no easy answer to this- if he allows her in his life it's misery, and setting boundaries with her may cause her to escalate- but in the long run he's taking better care of himself and the relationship.
I hope the information is helpful. Let me know if I can assist you again. Thank you for your post!